A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Answers
Given A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
First let us find find the volume of pipe, internal diameter is 20 cm
So we get the radius as r=d/ 2 = 20 / 2 = 10 cm = 1/10 m
Volume of pipe = t r^2 h
= T (1/10) ^2 h
volume of pipe = Th/ 10O
How to find volume of tank which is
cylindrical, So d = 10 m, r=d/2 = 5 m and height is 2
m
Volume of tank = mr ^2 h
= 1 (5)^2 x 2
Volume of tank = 50 TT
The farmer connects pipe to the tank, so
Volume of pipe = volume of tank = TTh/ 100 = 50 TT
h = 50 пх 100 / п
h = 5 km
Water travels at 3 km/hrFor 3 kms the time taken for water to travel is 1 hr
So for 5 kms time taken will be 5/3 hrs
5/3 x 60 = 100 minutes
The tank will be filled in 100 minutes
Answer:
The tank will be filled in 100 minutes
Step-by-step explanation:
First let us find find the volume of pipe,
internal diameter is 20 cm
So we get the radius as r = d / 2
= 20 / 2
= 10 cm
= 1 / 10 m
Volume of pipe = π r ^2 h
= π (1/10) ^2 h
volume of pipe = π h / 100
So d = 10 m, r = d / 2 = 5 m and height is 2 m
Volume of tank = π r ^2 h
to find volume of tank which is cylindrical,
= π (5) ^2 x 2
Volume of tank = 50 π
The farmer connects pipe to the tank, so
Volume of pipe = volume of tank
π h / 100 = 50 π
h = 50 π x 100 / π
h = 5 km
Water travels at 3 km / hr
For 3 kms the time taken for water to travel is 1 hr
So for 5 kms time taken will be 5 / 3 hrs
5 / 3 x 60 = 100 minutes
The tank will be filled in 100 minutes